Contact algorithms for the material point method in impact and penetration simulation

Abstract

SUMMARYThe inherent no-slip contact constraint in the standard material point method (MPM) creates a greater penetration resistance. Therefore, the standard MPM was not able to treat the problems involving impact and penetration very well. To overcome these deficiencies, two contact methods for MPM are presented and implemented in our 3D explicit MPM code, MPM3D. In MPM, the impenetrability condition may not satisfied on the redefined regular grid at the beginning of each time step, even if it has been imposed on the deformed grid at the end of last time step. The impenetrability condition between bodies is only imposed on the deformed grid in the first contact method, while it is imposed both on the deformed grid and redefined regular grid in the second contact method. Furthermore, three methods are proposed for impact and penetration simulation to determine the surface normal vectors that satisfy the collinearity conditions at the contact surface. The contact algorithms are verified by modeling the collision of two elastic rings and sphere rolling problems, and then applied to the simulation of penetration of steel ball and perforation of thick plate with a particle failure model. In the simulation of elastic ring collision, the first contact algorithm introduces significant disturbance into the total energy, but the second contact algorithm can obtain the stable solution by using much larger time step. It seems that both contact algorithms give good results for other problems, such as the sphere rolling and the projectile penetration.

Animation of crack propagation by means of an extended multi-body solver for the material point method

“…A similar approach was employed by Fan et al (2013), who uses this Eularian formulation to simulate contact for a Lagrangian mesh. Huang et al (2011) proposes a method targeted at MPM. They discretize each body to separate background grids, and an impenetrability condition is imposed with respect to the relative grid velocity to resolve collisions.…”

“…When these particle constraints break, each body must interact with every other body in the simulation. Section 3.1 first describes a two-body collision scheme founded upon the work of Huang et al (2011). This two-body algorithm is a reformulation of the same method they present in their paper, but we introduce a different notation which we use for our extension to N-body collisions.…”

“…For two bodies, conservation of momentum can only occur when the surface normals are collinear. In general this is not the case, and Huang et al (2011) suggest multiple methods to ensure that this condition is kept. However, when increasing the number of colliding bodies to more than two, we were not able to adapt their algorithm to keep momentum conserved (as collinearity does not scale to more than two vectors).…”

“…where we use the center of mass velocity Huang et al (2011). Thus, two grids are considered to be colliding at a grid node if…”

“…The focus of this paper is on simulation of bodies with a single crack, and where the crack propagation is dominated by an opening mode. The pieces from a fractured body are allowed to interact freely in the simulation, and we also present an extension to the contact algorithm by Huang et al (2011) to allow for arbitrarily many colliding bodies in the same solver.…”